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The new head of the National Center for Science Education promises to "fight the good fight" against attacks on...
Analyses of the H7N9 strains isolated from four new cases show that the virus is evolving rapidly, heightening anxiety...
In 2009, Jack Szostak shared a Nobel Prize for his part in discovering the role of telomeres, the end bits of...
Science has exposed a thriving academic black market in China involving shady agencies, corrupt scientists, and...
Paper-selling agencies flourish in the aura of reputable businesses. For some scientists, it may be difficult to tell...
Featuring the first lunar rover in 40 years, Chang'e-3 is seen as an important milestone on China's quest to send a...
Data collected by satellites and floating probes have chronicled a 2-decade rise in the temperature and thickness of a...
Cholesterol, the artery-clogging molecule that contributes to cardiovascular disease, has another nasty trick up its...
- 27 November 2013 12:59 pm , Vol. 342 , #6162
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Stay in the Tub, Archimedes
21 November 2003 (All day)
Perhaps it wouldn't make him run naked through the streets shouting "eureka," but Archimedes would no doubt be pleased that one of his puzzles has been completely solved more than 2000 years later.
In the third century B.C.E., Archimedes posed a geometric mindbender: How can one get a particular set of 14 irregular triangles and quadrilaterals to fit together into one big square? Finding one solution isn't that hard, but nobody knew how many solutions there are. "When you first start looking at it, it seems like it might have thousands and thousands of solutions," says mathematician Ed Pegg, who works at Wolfram Research, a mathematics software company in Champaign, Illinois.
But just this month, puzzlemaker Bill Cutler of Palatine, Illinois, put the 2-millennium-old poser to rest. Using a computer's brute force, Cutler figured out by trial and error that there were only 536 solutions to the puzzle, excluding rotating and reflecting the final assembled square. One element that made the problem tractable was that there are three pairs of pieces that need always be together--one side of each of those pieces is a length that only fits together with its partner.
That constraint as well as the fact that there were obviously lots of solutions limited Archimedes' puzzle's appeal, says Pegg. "It really wasn't all that good of a puzzle," he says. "So it went by the wayside." Nevertheless, he thinks that the solution to the ancient problem is a victory.